Conserved Currents in Supersymmetric Quantum Cosmology?

TL;DR

This paper explores the possibility of defining conserved currents in supersymmetric quantum cosmology models, finding that such currents are generally not well-defined except in simple cases, and discusses implications for quantum states and classical limits.

Contribution

It investigates the existence of conserved currents in supersymmetric minisuperspaces, highlighting limitations and connections to Wheeler-DeWitt equations and quantum states.

Findings

Conserved currents are generally not well-defined in supersymmetric models.

In simple scenarios, conserved currents can be established.

The Hartle-Hawking state can be identified in supersymmetric quantum cosmology.

Abstract

In this paper we investigate whether conserved currents can be sensibly defined in supersymmetric minisuperspaces. Our analysis deals with k=1 FRW and Bianchi class--A models. Supermatter in the form of scalar supermultiplets is included in the former. Moreover, we restrict ourselves to the first-order differential equations derived from the Lorentz and supersymmetry constraints. The ``square-root'' structure of N=1 supergravity was our motivation to contemplate this interesting research. We show that conserved currents cannot be adequately established except for some very simple scenarios. Otherwise, conservation equations may only be obtained from Wheeler-DeWitt--like equations, which are derived from the supersymmetric algebra of constraints. Two appendices are included. In appendix A we describe some interesting features of quantum FRW cosmologies with complex scalar fields when supersymmetry is present. In particular, we explain how the Hartle-Hawking state can now be satisfactorily identified. In appendix B we initiate a discussion about the retrieval of classical properties from supersymmetric quantum cosmologies.